Chapter 5.4, Problem 7Q

To determine

To calculate:

System of linear equation by substitution.

Answer to Problem 7Q

Solution is checked and value are $x=2,y=2$

Explanation of Solution

Given information:

  $\begin{array}{l}x+y=4\\ -3x-y=-8\end{array}$

Calculation:

Given equations are:

  $\begin{array}{l}x+y=\mathrm{4...}\left(i\right)\\ -3x-y=-\mathrm{8...}\left(ii\right)\end{array}$

After simplifying equations become:

  $x=4-y\mathrm{...}\left(iii\right)$

Put the eq. $\left(iii\right)$ in eq. $\left(i\right)$ :

  $\begin{array}{l}-3\left(4-y\right)-y=-8\\ -12+3y-y=-8\end{array}$

Now solve $y$ ,

  $\begin{array}{l}-12+3y-y=-8\\ -12+2y=-8\\ 2y=-8+12\\ 2y=4\end{array}$

Divide by $2$ on both sides,

  $\begin{array}{l}\frac{2y}{2}=\frac{4}{2}\\ y=2\end{array}$

Put the $y=2$ in eq. $\left(iii\right)$ to find out $x$

  $\begin{array}{l}x=4-y\\ x=4-2\\ x=2\end{array}$

For checking the obtained solutions,

Put the value of $x,y$ in any equation,

  $\begin{array}{l}x=4-y\\ 2=4-2\\ 2=2\end{array}$

Hence solution is checked.